Announcement A total of 5 (five) late days are allowed for projects. Office hours

Announcement A total of 5 (five) late days are allowed for projects. Office hours Me: 3:50-4:50pm Thursday (or by appointment) Jake: 12:30-1:30PM Monday and Wednesday

Image Formation Digital Camera Film Alexei Efros slide The Eye

Image Formation Let s design a camera Idea 1: put a piece of film in front of an object Do we get a reasonable image? Steve Seitz s slide

Pinhole Camera Add a barrier to block off most of the rays This reduces blurring The opening known as the aperture How does this transform the image? Steve Seitz s slide

Camera Obscura The first camera 5 th B.C. Aristotle, Mozi (Chinese: 墨子 ) How does the aperture size affect the image? http://en.wikipedia.org/wiki/pinhole_camera

Shrinking the aperture Why not make the aperture as small as possible? Less light gets through Diffraction effects...

Shrinking the aperture

Shrinking the aperture Sharpest image is obtained when: d 2 f d is diameter, f is distance from hole to film λ is the wavelength of light, all given in metres. Example: If f = 50mm, λ = 600nm (red), d = 0.36mm Srinivasa Narasimhan s slide

Pinhole cameras are popular Jerry Vincent's Pinhole Camera

Impressive Images Jerry Vincent's Pinhole Photos

What s wrong with Pinhole Cameras? Low incoming light => Long exposure time => Tripod KODAK Film or Paper Bright Sun Cloudy Bright TRI-X Pan 1 or 2 seconds 4 to 8 seconds T-MAX 100 Film 2 to 4 seconds 8 to 16 seconds KODABROMIDE Paper, F2 2 minutes 8 minutes http://www.kodak.com/global/en/consumer/education/lessonplans/pinholecamera/pinholecanbox.shtml

What s wrong with Pinhole Cameras People are ghosted

What s wrong with Pinhole Cameras People become ghosts!

Pinhole Camera Recap Pinhole size (aperture) must be very small to obtain a clear image. However, as pinhole size is made smaller, less light is received by image plane. If pinhole is comparable to wavelength of incoming light, DIFFRACTION effects blur the image!

What s the solution? Lens circle of confusion A lens focuses light onto the film There is a specific distance at which objects are in focus other points project to a circle of confusion in the image Changing the shape of the lens changes this distance Steve Seitz s slide

Thin lens optics Simplification of geometrical optics for well-behaved lenses All parallel rays converge to one point on a plane located at the focal length f f All rays going through the center are not deviated Hence same perspective as pinhole Frédo Durand s slide

Demo! http://www.phy.ntnu.edu.tw/java/lens/lens_e.html (by Fu-Kwun Hwang )

Thin lens formula D f D Frédo Durand s slide

Thin lens formula Similar triangles everywhere! D f D Frédo Durand s slide

Thin lens formula Similar triangles everywhere! y /y = D /D y D f D y Frédo Durand s slide

Thin lens formula Similar triangles everywhere! D D f y y /y = D /D y /y = (D -f)/d y Frédo Durand s slide

Thin lens formula 1 + 1 = 1 D D f D f D The focal length f determines the lens s ability to bend (refract) light. It is a function of the shape and index of refraction of the lens. Frédo Durand s slide

Film camera aperture & shutter scene lens & motor film YungYu Chuang s slide

Film camera Still Life, Louis Jaques Mande Daguerre, 1837 Srinivasa Narasimhan s slide

Before Film was invented Lens Based Camera Obscura, 1568 Srinivasa Narasimhan s slide

Silicon Image Detector Silicon Image Detector, 1970 Shree Nayar s slide

Digital camera aperture & shutter scene lens & motor sensor array A digital camera replaces film with a sensor array Each cell in the array is a light-sensitive diode that converts photons to electrons YungYu Chuang s slide

SLR (Single-Lens Reflex) Reflex (R in SLR) means that we see through the same lens used to take the image. Not the case for compact cameras YungYu Chuang s slide

SLR view finder Prism Your eye Mirror (flipped for exposure) Film/sensor Light from scene Mirror (when viewing) lens YungYu Chuang s slide

Compound Lens System d final image i2 f2 o2 i 1 f1 object o 1 image plane intermediate lens 2 virtual image lens 1 Rule : Image formed by first lens is the object for the second lens. If d 0, the combined focal length f is f f1 f2 f f 1 2 Srinivasa Narasimhan s slide

Field of View (FoV) vs Focal Length Canon EF-S 60mm f/2.8 Canon EF 100mm f/2.8 Canon EF 180mm f/3.5

Field of View (FoV) vs Focal Length 24mm 50mm 135mm Frédo Durand s slide

Field of View (FoV) vs Focal Length i o Scene w α Sensor f Gaussian Lens Formula: 1 i 1 o 1 f Field of View: α = 2arctan(w/(2i)) 2arctan(w/(2f)) Example: w = 30mm, f = 50mm => α 33.4º Question: How does FoV change when we focus on closer objects?

Depth of Field Changing the aperture size affects depth of field. A smaller aperture increases the range in which the object is approximately in focus

Aperture Aperture is the diameter of the lens opening, usually specified by f-stop, f/d, a fraction of the focal length. f/2.0 on a 50mm means that the aperture is 25mm f/2.0 on a 100mm means that the aperture is 50mm When a change in f-stop occurs, the light is either doubled or cut in half. Lower f-stop, more light (larger lens opening) Higher f-stop, less light (smaller lens opening) YungYu Chuang s slide

f o i 1 1 1 d aperture diameter aperture f o i 1 ' 1 ' 1 Gaussian Law: Blur Circle, b ') ( ) ( ) ' ( ) ' ( o o f o f f o f i i Blur Circle Diameter : ) ' ( ) ' ( ' i i f d i i i d b i i' o' o sensor d f f-stop: # F-stop

F-stop Canon EF-S 60mm f/2.8 Canon EF 100mm f/2.8 Canon EF 180mm f/3.5

Exposure Two main parameters: Aperture (in f stop) shutter speed (in fraction of a second) See http://www.photonhead.com/simcam/

Effects of shutter speeds Slower shutter speed => more light, but more motion blur Faster shutter speed freezes motion YungYu Chuang s slide

Color So far, we ve only talked about monochrome sensors. Color imaging has been implemented in a number of ways: Field sequential Multi-chip Color filter array X3 sensor YungYu Chuang s slide

Field sequential YungYu Chuang s slide

Field sequential YungYu Chuang s slide

Field sequential YungYu Chuang s slide

Prokudin-Gorskii (early 1900 s) Lantern projector http://www.loc.gov/exhibits/empire/ YungYu Chuang s slide

Prokudin-Gorskii (early 1990 s) YungYu Chuang s slide

Multi-chip wavelength dependent YungYu Chuang s slide

Embedded color filters Color filters can be manufactured directly onto the photodetectors. YungYu Chuang s slide

Color filter array Bayer pattern Color filter arrays (CFAs)/color filter mosaics YungYu Chuang s slide

Color filter array Kodak DCS620x Color filter arrays (CFAs)/color filter mosaics CMY YungYu Chuang s slide

Why CMY CFA might be better YungYu Chuang s slide

Bayer s pattern YungYu Chuang s slide

Demosaicking CFA s bilinear interpolation original input linear interpolation YungYu Chuang s slide

Demosaicking CFA s Median-based interpolation (Freeman) 1. Linear interpolation 2. Median filter on color differences YungYu Chuang s slide

Demosaicking CFA s Median-based interpolation (Freeman) original input linear interpolation color difference (e.g. G-R) YungYu Chuang s slide median filter (kernel size 5) Reconstruction (G=R+filtered difference)

Demosaicking CFA s Generally, Freeman s is the best, especially for natural images. YungYu Chuang s slide

Foveon X3 sensor light penetrates to different depths for different wavelengths multilayer CMOS sensor gets 3 different spectral sensitivities YungYu Chuang s slide

Color filter array red green blue output YungYu Chuang s slide

X3 technology red green blue output YungYu Chuang s slide

Foveon X3 sensor Bayer CFA X3 sensor YungYu Chuang s slide

Cameras with X3 Sigma SD10, SD9 Polaroid X530 YungYu Chuang s slide

Sigma SD9 vs Canon D30 YungYu Chuang s slide

Color processing After color values are recorded, more color processing usually happens: White balance Non-linearity to approximate film response or match TV monitor gamma YungYu Chuang s slide

Auto White Balance warmer automatic white balance YungYu Chuang s slide

Auto White Balance The auto white balance was unable to find a white reference, resulting in dull and artificial colors. The auto white balance got it right this time in a very similar scene because it could use the clouds as its white reference. http://www.dpreview.com/learn/?/glossary/digital_imaging/white_balance_01.htm

Manual white balance white balance with the white book white balance with the red book YungYu Chuang s slide

Lens related issues: Coumpound Thick Lens principal planes nodal points thickness

Lens related issues: Vignetting Vignetting L3 L 2 L 1 B A more light from A than B!

Lens related issues: Vignetting Vignetting L3 L 2 L 1 B A more light from A than B! original corrected Goldman & Seitz ICCV 2005

Lens related issues: Chromatic Abberation Lens has different refractive indices for different wavelengths. http://www.dpreview.com/learn/?/glossary/optical/chromatic_aberration_01.htm Special lens systems using two or more pieces of glass with different refractive indexes can reduce or eliminate this problem.

Lens related issues: Distortion No distortion Pin cushion Barrel Radial distortion of the image Caused by imperfect lenses Deviations are most noticeable for rays that pass through the edge of the lens Steve Seitz s slide

Correcting radial distortion from Helmut Dersch Steve Seitz s slide

Digital camera review website http://www.dpreview.com/ http://www.imaging-resource.com/ http://www.steves-digicams.com/